Solution Found!
In ice-cream making, the ingredients are kept below 0.0°C
Chapter 14, Problem 109P(choose chapter or problem)
Problem 109P
In ice-cream making, the ingredients are kept below 0.0°C in an ice-salt bath, (a) Assuming that NaCl dissolves completely and forms an ideal solution, what mass of it is needed to lower the melting point of 5.5 kg of ice to −5.0°C? (b) Given the same assumptions as in part (a), what mass of CaCl2 is needed?
Questions & Answers
QUESTION:
Problem 109P
In ice-cream making, the ingredients are kept below 0.0°C in an ice-salt bath, (a) Assuming that NaCl dissolves completely and forms an ideal solution, what mass of it is needed to lower the melting point of 5.5 kg of ice to −5.0°C? (b) Given the same assumptions as in part (a), what mass of CaCl2 is needed?
ANSWER:
Solution 109P:
Step 1: (a)
Here, we are going to calculate the mass of NaCl is needed to lower the melting point of 5.5 kg of ice to −5.0°C.
Given that,
NaCl is a strong electrolyte solution. Thus, it dissociates into two particles.
Therefore,
The freezing point depression of NaCl is given by:
Given that,
= -5.0
=1.86 /m
Therefore, the molality of NaCl is obtained as follows:
= 1.344 m
We Know that
1.34 mol/kg
Moles of NaCl = 7.392 mol
Similarly, the molar mass of NaCl = 58.44 g/mol
Therefore, the mass of NaCl needed = 7.392 mol 58.44 g/mol
= 431.98 g